Finite Group Databasebeta

← #6614902

Subgroups — #6614902

Order 512.

2032 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic, complemented
3#33277C211yesmaximal, characteristic, complemented
4#33171C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29178C211yesmaximal, characteristic, complemented
7#29071C214yesmaximal, complemented
8#28975C214yesmaximal, complemented
9#28615C211yesmaximal, characteristic, complemented
10#28551C214yesmaximal, complemented
11#27973C211yesmaximal, characteristic, complemented
12#27877C211yesmaximal, characteristic, complemented
13#25903C211yesmaximal, characteristic, complemented
14#25599C211yesmaximal, characteristic, complemented
15#23127C214yesmaximal, complemented
16C4×#486C211yesmaximal, characteristic, complemented
17#21401C211yesmaximal, characteristic, complemented
18C2×#1990C211yesmaximal, characteristic, complemented
19C4×C8×D4C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#548—21no—
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#466C2214yes—
28C2×C8×D4C2212yes—
29C22×C4×C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2859C2211yescharacteristic
32#2858C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2856C2211yescharacteristic
37#2566—21no—
38#2545—21no—
39#2512—21no—
40#2512C2212yes—
41#2504—21no—
42#2500—21no—
43#2491—21no—
44#2491C2212yes—
45#2452—21no—
46#2452C2212yes—
47#2436—21no—
48#2432—21no—
49#2422—21no—
50#2422C2212yes—
51#2416—21no—
52#2416—21no—
53#2416C2212yes—
54#2416C2212yes—
55#2361—21no—
56#2361—21no—
57#2361C2212yes—
58#2361C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2086C2214yes—
65#2075C2214yes—
66#2071C2214yes—
67#2054C2214yes—
68#2023C2214yes—
69#1999C2214yes—
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1970C2214yes—
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1934C2214yes—
83#1934C2214yes—
84#1934C2214yes—
85#1934C2214yes—
86#1918C2214yes—
87#1918C2214yes—
88#1893C2214yes—
89#1893C2214yes—
90#1879C2214yes—
91#1879C2214yes—
92#1874C2214yes—
93#1874C2214yes—
94#1845C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97C8×C4⋊C4C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99C4×#102C2214yes—
100C4×#102C2214yes—
101C8×C22⋊C4C2212yes—
102C8×C22⋊C4C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C2×#340C2214yes—
106C42×C8C2211yescharacteristic
107C22×#41—21no—
108C23×Q8—21no—
109C22×D8C2314yes—
110C23×C8C2312yes—
111C23×C8C2312yes—
112#553—48no—
113#548—48no—
114#532—24no—
115#532—42no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#127C2311yescharacteristic
125C2×#126—22no—
126C2×#125—21no—
127C2×#124—22no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×#123—22no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—22no—
134C2×#121—22no—
135C2×#121—22no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—21no—
143C2×#121C2312yes—
144C2×#121C2312yes—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×C4×Q8—21no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#493—42no—
167#486—24no—
168#486—42no—
169#466—216no—
170C8×D4—28no—
171C2×#107C2314yes—
172C2×C4⋊C8C2312yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C4×C8—42no—
182C2×C4×C8—42no—
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2312yes—
188C2×C4×C8C2312yes—
189C2×C4×C8C2312yes—
190C2×C4×C8C2312yes—
191#397—22no—
192#397—22no—
193#396—22no—
194#396—22no—
195#396—22no—
196#396—22no—
197#394—22no—
198#394—22no—
199#394—22no—
200#394—22no—
201#393—22no—
202#393—22no—
203#391—21no—
204#391—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#390C2312yes—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#384—21no—
242#384—21no—
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#384C2312yes—
246#384C2311yescharacteristic
247#384C2311yescharacteristic
248#382—21no—
249#382—21no—
250#380—21no—
251#380—21no—
252#380C2312yes—
253#380C2312yes—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2311yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C43C2311yescharacteristic
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—82no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—22no—
285C22×Q8—44no—
286C22×Q8—44no—
287C22×Q8—82no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C2×D411yescharacteristic
297C22×D4C2412yes—
298C22×D4C2412yes—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C2×D8—28no—
310C2×D8—44no—
311C2×D8—44no—
312C22×C8—24no—
313C22×C8—42no—
314C22×C8—42no—
315C22×C8—42no—
316C22×C8—42no—
317C22×C8#4118yescomplemented
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—42no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8#4114yes—
330#127—22no—
331#127—22no—
332#127—22no—
333#127—22no—
334#126—48no—
335#125—44no—
336#124—44no—
337#124—48no—
338#124—44no—
339#124—82no—
340#123—48no—
341C22⋊Q8—44no—
342C22⋊Q8—48no—
343#121—28no—
344#121—28no—
345#121—24no—
346#121—42no—
347#121—44no—
348#121—48no—
349#121—48no—
350#121—44no—
351#121—44no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—82no—
357C4×Q8—44no—
358C4×D4—24no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—42no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—48no—
365C4×D4—48no—
366C4×D4—44no—
367C4×D4—82no—
368C4×D4D818yescomplemented
369#117—44no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—82no—
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2×D411yescharacteristic
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449#107—28no—
450C4⋊C8—24no—
451#102—28no—
452#102—28no—
453#102—28no—
454#102—44no—
455#102—44no—
456#102—44no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C4×C8—24no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—42no—
465C4×C8—42no—
466C4×C8—42no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479#95C2×D411yescharacteristic
480#95C2×D411yescharacteristic
481C24—22no—
482C24—22no—
483C24C22×D411yescharacteristic
484C24C22×D411yescharacteristic
485#41—816no—
486C2×Q8—24no—
487C2×Q8—44no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—82no—
495C2×Q8—816no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—24no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4C2×D814yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—82no—
560C22×C4—82no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4C2×D814yes—
566C22×C4C2×D814yes—
567C22×C4#13514yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C2×#4114yes—
581C22×C4C2511yescharacteristic
582D8—88no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—48no—
594C2×C8—48no—
595C2×C8C2×#4114yes—
596C2×C8C2×#4114yes—
597C4⋊C4—22no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—82no—
624C4⋊C4—82no—
625C4⋊C4C2×D814yes—
626C4⋊C4C2×#4114yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C22⋊C4—82no—
651C22⋊C4C2×D814yes—
652C22⋊C4C2×D814yes—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—22no—
666C42—44no—
667C42—44no—
668C42C2×D814yes—
669C42C2×#4112yes—
670C42H(5,𝔽2)12yes—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23#53212yes—
696C23C22×D812yes—
697C23C22×D812yes—
698C23C2×#13512yes—
699C23C23×D411yescharacteristic
700Q8—48no—
701Q8—88no—
702Q8—84no—
703D4—28no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—44no—
708D4—88no—
709D4—88no—
710D4—88no—
711D4—84no—
712D4—84no—
713D4—84no—
714D4—84no—
715D4—164no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—24no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—88no—
767C2×C4—88no—
768C2×C4—164no—
769C2×C4—164no—
770C2×C4#53212yes—
771C2×C4#54612yes—
772C2×C4#54612yes—
773C2×C4C22×D812yes—
774C2×C4C22×D812yes—
775C2×C4C22×D812yes—
776C2×C4C22×D812yes—
777C2×C4C22×D812yes—
778C2×C4C2×#13512yes—
779C2×C4C2×#13512yes—
780C2×C4#57712yes—
781C2×C4#57712yes—
782C2×C4C22×#4111yescharacteristic
783C2×C4C22×#4112yes—
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C2×C4#58512yes—
786C8—24no—
787C8—24no—
788C8—42no—
789C8—42no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22#316914yes—
818C22C2×#53211yescharacteristic
819C22C2×#54611yescharacteristic
820C22#350011yescharacteristic
821C22C23×D811yescharacteristic
822C22C22×#13511yescharacteristic
823C22C2×#57711yescharacteristic
824C22C2×#57711yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4—44no—
835C4—41no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4#329414yes—
842C4#330114yes—
843C4#348012yes—
844C4#350512yes—
845C2—24no—
846C2—42no—
847C2—162no—
848C2—162no—
849C2#3639611yescharacteristic
850C2C2×#316911yescharacteristic
851C2#6071611yescharacteristic
852C2C2×#329411yescharacteristic
853C2C2×#330111yescharacteristic
854C2#6252911yescharacteristic
855C2#6253211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #36182C2semidirect
2. #36122C2semidirect
3. #33277C2semidirect
4. #33171C2semidirect
5. #33042C2semidirect
6. #29178C2semidirect
7. #29071C2semidirect
8. #28975C2semidirect
9. #28615C2semidirect
10. #28551C2semidirect
11. #27973C2semidirect
12. #27877C2semidirect
13. #25903C2semidirect
14. #25599C2semidirect
15. #23127C2semidirect
16. C4×#486C2semidirect
17. #21401C2semidirect
18. C2×#1990C2semidirect
19. C4×C8×D4C2semidirect
317. C22×C8#41semidirect
368. C4×D4D8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#361822
#361222
#332772
#331712
#330422
#291782
#290712
#289752
#286152
#285512
#279732
#278772
#259032
#255992
#231272
C4×#4862
#214012
C2×#19902
C4×C8×D42